Specifically, I see this as a general priority list when determining which things to use when trying to evoke an emotional reaction to an image. I showed how even a playful color scheme was ineffective when the other elements were stacked against it:

Note that I used the value and color composition to undermine the softening effects the color scheme might have---red tucked into every corner, dead colors in the flesh surrounding the mouth, light/color lifting the eyes out from the masses of the face, etc.

A few people asked for more about this subject, so this time let's contrast the power of style in this hierarchy vs. the other elements:

See how easily a change of style makes "terrifying" become "spooky lite"? Style fundamentally changes the equation so that compensating for it with the other factors becomes difficult.

"But Sam," some might say, "these textures are different than the original. Isn't that cheating since you're changing two things and not one?" That's one of the reasons why style is at the top of the list. Style can dictate what choices are possible with all the other elements. If this character was placed in a world with smooth-textured, cute characters with giant eyes, the proportions and surfaces of this guy would appear pretty extreme and dark in comparison. So by that measurement, these are the textures of the original as interpreted through this style.In this way, each item in this list can set the context for the thing after it. If I used a gritty style, but then the subject was a happy puppy, then every choice I made with lighting, value composition, and even surfaces or color would be seen through the lens of that subject matter. The subject matter also dictates what range of surfaces can be used---I can't change the fur of a puppy to something else or it won't be a puppy anymore. And because it's a happy puppy, covering the fur with slime merely makes the puppy look a little naughty.I use the word "can" because sometimes design decisions themselves are neutral or weak, like with lighting, which can be easily used in a way that doesn't modify the rest of the list. Sometimes keeping one element neutral so another element can show through more strongly is the way to go. Likewise, some subjects are just neutral by nature and we have to push on other factors to say something about them.

Shifting every element (including style) to communicate a clear message

Because of the context-setting ability of these priorities, while I sometimes use each element in concert to reinforce a message, I will more often use contrasts within each element on this list to add nuance and interest to the message of an image. Putting a scary character in a scary style with scary surfaces and scary lighting is definitely a clear message, if a bit predictable. However, a lovable character in a harsh style with lighting that makes us uneasy but surfaces that lull us into sense of comfort, becomes a really interesting image that can be scary in a different way. So long as each thing really sets the context for the next and there's some internal consistency within any single element, you can create enough cognitive dissonance to engage people's brains without confusing them. Just changing one thing is often enough to add this kind of interest, which is probably a safer way to go if you're still trying to figure this whole thing out.

Mixed messages---appropriate for a more nuanced character

This is all just my opinion and experience though, and I'd love to hear your arguments if you have a different line of reasoning!